Part I. How Linear Equations relate to Tables Of Values

Equations as Relationships

The equation of a line expresses a relationship between x and y values on the coordinate plane. For instance, the equation y = x expresses a relationship where every x value has the exact same y value. The
equation y = 2x expresses a relationship in which every y value is double the x value, and y = x +1 expresses a relationship in which every y value is 1 greater than the x value.

So what about a Table Of Values?

Since, as we just wrote, every equation is a relationship of x and y values, we can create a table of values for any line, these are just the x and y values that are true for the given line. In other words, a table of values is simply some of the points that are on the line.

Let's See Some Examples

Example 1

Equation: y = x + 1

Table of Values

X Value

Equation

Y value

y = x +1

3

y = (3) +1

4

4

y = (4) +1

5

5

y = (5) +1

6

6

y = (6) + 1

7

Example 2

Equation: y = 3x + 2

Table of Values

X Value

Equation

Y value

y = 3x + 2

1

y = 3(1) + 2

5

2

y = 3(2) + 2

7

3

y = 3(3) + 2

11

4

y = 3(4) + 2

14

So, to create a table of values for a line, just pick a set of x values, substitute them into the equation and evaluate to get the y values.

An Optional step, if you want, you can omit the middle column from your table, since the table of values is really just the x and y pairs. (We used the middle column simply to help us get the y values)

An Optional step, if you want, you can omit the middle column from your table, since the table of values is really just the x and y pairs .(We used the middle column simply to help us get the y values)

An Optional step, if you want, you can omit the middle column from your table, since the table of values is really just the x and y pairs. (We used the middle column simply to help us get the y values)

The reason that this table could not represent the equation of a line is because the slope is inconsistent. For instance the slope of the 2 points at the top of the table (0,1) and (1,3) is different from the slope at the bottom (2,8) and (3,11)